package com.jellyfishumbrella.noise;

import com.jellyfishumbrella.GL.Vector3d;

/**
 * This class implements Ken Perlin's "simplex noise" algorithm.  It is based on an
 * implementation is by Stefan Gustavson, found in his article, "Simplex Noise Demystified"
 * (http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf).  It has been modified
 * to improve performance, and methods to calculate the gradient of the noise function and
 * a vector valued noise function have been added.
 * <p>
 * This is a function which varies smoothly between -1.0 and 1.0, with all of the variation
 * happening on a length scale of about 1.  Typically, you will want to add several octaves
 * of this function together to create a fractal noise function.  Methods are also provided
 * for calculating the gradient of the noise function, and a closely related noise function
 * which is vector valued.
 * <p>
 * Note: it is generally recommended to use the {@link Noise} class instead of calling this
 * one directly, since that allows the preferred noise generator to be changed.
 */

public class SimplexNoise { // Simplex noise in 2D, 3D and 4D
    private static Grad grad3[] = { new Grad(1, 1, 0),
            new Grad(-1, 1, 0), new Grad(1, -1, 0),
            new Grad(-1, -1, 0), new Grad(1, 0, 1), new Grad(-1, 0, 1),
            new Grad(1, 0, -1), new Grad(-1, 0, -1), new Grad(0, 1, 1),
            new Grad(0, -1, 1), new Grad(0, 1, -1), new Grad(0, -1, -1) };
    private static Grad grad4[] = { new Grad(0, 1, 1, 1),
            new Grad(0, 1, 1, -1), new Grad(0, 1, -1, 1),
            new Grad(0, 1, -1, -1), new Grad(0, -1, 1, 1),
            new Grad(0, -1, 1, -1), new Grad(0, -1, -1, 1),
            new Grad(0, -1, -1, -1), new Grad(1, 0, 1, 1),
            new Grad(1, 0, 1, -1), new Grad(1, 0, -1, 1),
            new Grad(1, 0, -1, -1), new Grad(-1, 0, 1, 1),
            new Grad(-1, 0, 1, -1), new Grad(-1, 0, -1, 1),
            new Grad(-1, 0, -1, -1), new Grad(1, 1, 0, 1),
            new Grad(1, 1, 0, -1), new Grad(1, -1, 0, 1),
            new Grad(1, -1, 0, -1), new Grad(-1, 1, 0, 1),
            new Grad(-1, 1, 0, -1), new Grad(-1, -1, 0, 1),
            new Grad(-1, -1, 0, -1), new Grad(1, 1, 1, 0),
            new Grad(1, 1, -1, 0), new Grad(1, -1, 1, 0),
            new Grad(1, -1, -1, 0), new Grad(-1, 1, 1, 0),
            new Grad(-1, 1, -1, 0), new Grad(-1, -1, 1, 0),
            new Grad(-1, -1, -1, 0) };
    private static short p[] = { 151, 160, 137, 91, 90, 15, 131, 13,
            201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69,
            142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120,
            234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11,
            32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136,
            171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166, 77,
            146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220,
            105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25,
            63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18,
            169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109,
            198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202,
            38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47,
            16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248,
            152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172,
            9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232,
            178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193,
            238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235,
            249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157,
            184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138,
            236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195,
            78, 66, 215, 61, 156, 180 };
    // To remove the need for index wrapping, double the permutation table length
    private static short perm[] = new short[512];
    private static short permMod12[] = new short[512];
    static {
        for (int i = 0; i < 512; i++) {
            perm[i] = p[i & 255];
            permMod12[i] = (short) (perm[i] % 12);
        }
    }
    // A lookup table to traverse the simplex around a given point in 4D.
    // Details can be found where this table is used, in the 4D noise method.
    private static int simplex[][] = { { 0, 1, 2, 3 }, { 0, 1, 3, 2 },
            { 0, 0, 0, 0 }, { 0, 2, 3, 1 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 1, 2, 3, 0 },
            { 0, 2, 1, 3 }, { 0, 0, 0, 0 }, { 0, 3, 1, 2 },
            { 0, 3, 2, 1 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 1, 3, 2, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 1, 2, 0, 3 }, { 0, 0, 0, 0 },
            { 1, 3, 0, 2 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 2, 3, 0, 1 }, { 2, 3, 1, 0 },
            { 1, 0, 2, 3 }, { 1, 0, 3, 2 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 2, 0, 3, 1 },
            { 0, 0, 0, 0 }, { 2, 1, 3, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 2, 0, 1, 3 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 3, 0, 1, 2 },
            { 3, 0, 2, 1 }, { 0, 0, 0, 0 }, { 3, 1, 2, 0 },
            { 2, 1, 0, 3 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 0, 0, 0, 0 }, { 3, 1, 0, 2 }, { 0, 0, 0, 0 },
            { 3, 2, 0, 1 }, { 3, 2, 1, 0 } };
    // Skewing and unskewing factors for 2, 3, and 4 dimensions
    private static final double F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
    private static final double G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
    private static final double F3 = 1.0 / 3.0;
    private static final double G3 = 1.0 / 6.0;
    private static final double F4 = (Math.sqrt(5.0) - 1.0) / 4.0;
    private static final double G4 = (5.0 - Math.sqrt(5.0)) / 20.0;

    // This method is a *lot* faster than using (int)Math.floor(x)
    private static int fastfloor(double x) {
        return x > 0 ? (int) x : (int) x - 1;
    }

    private static double dot(Grad g, double x, double y) {
        return g.x * x + g.y * y;
    }

    private static double dot(Grad g, double x, double y, double z) {
        return g.x * x + g.y * y + g.z * z;
    }

    private static double dot(Grad g, double x, double y, double z,
            double w) {
        return g.x * x + g.y * y + g.z * z + g.w * w;
    }

    /**
     * Calculate the noise value at a point in 2D space.
     */
    public static double noise(double xin, double yin) {
        double n0, n1, n2; // Noise contributions from the three corners
        // Skew the input space to determine which simplex cell we're in
        double s = (xin + yin) * F2; // Hairy factor for 2D
        int i = fastfloor(xin + s);
        int j = fastfloor(yin + s);
        double t = (i + j) * G2;
        double X0 = i - t; // Unskew the cell origin back to (x,y) space
        double Y0 = j - t;
        double x0 = xin - X0; // The x,y distances from the cell origin
        double y0 = yin - Y0;
        // For the 2D case, the simplex shape is an equilateral triangle.
        // Determine which simplex we are in.
        int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
        if (x0 > y0) {
            i1 = 1;
            j1 = 0;
        } // lower triangle, XY order: (0,0)->(1,0)->(1,1)
        else {
            i1 = 0;
            j1 = 1;
        } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
        // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
        // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
        // c = (3-sqrt(3))/6
        double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        double y1 = y0 - j1 + G2;
        double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
        double y2 = y0 - 1.0 + 2.0 * G2;
        // Work out the hashed gradient indices of the three simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int gi0 = permMod12[ii + perm[jj]];
        int gi1 = permMod12[ii + i1 + perm[jj + j1]];
        int gi2 = permMod12[ii + 1 + perm[jj + 1]];
        // Calculate the contribution from the three corners
        double t0 = 0.5 - x0 * x0 - y0 * y0;
        if (t0 < 0)
            n0 = 0.0;
        else {
            t0 *= t0;
            n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
        }
        double t1 = 0.5 - x1 * x1 - y1 * y1;
        if (t1 < 0)
            n1 = 0.0;
        else {
            t1 *= t1;
            n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
        }
        double t2 = 0.5 - x2 * x2 - y2 * y2;
        if (t2 < 0)
            n2 = 0.0;
        else {
            t2 *= t2;
            n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to return values in the interval [-1,1].
        return 70.0 * (n0 + n1 + n2);
    }

    /**
     * Calculate the gradient of the noise function at a point in 2D space.
     *
     * @param gradient      this is set equal to the gradient of the noise function
     * @param xin           the x coordinate at which to evaluate the function
     * @param yin           the y coordinate at which to evaluate the function
     */
	public static void noiseGradient(Vector3d gradient, double xin, double yin) {
        // Skew the input space to determine which simplex cell we're in
        double s = (xin + yin) * F2; // Hairy factor for 2D
        int i = fastfloor(xin + s);
        int j = fastfloor(yin + s);
        double t = (i + j) * G2;
        double X0 = i - t; // Unskew the cell origin back to (x,y) space
        double Y0 = j - t;
        double x0 = xin - X0; // The x,y distances from the cell origin
        double y0 = yin - Y0;
        // For the 2D case, the simplex shape is an equilateral triangle.
        // Determine which simplex we are in.
        int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
        if (x0 > y0) {
            i1 = 1;
            j1 = 0;
        } // lower triangle, XY order: (0,0)->(1,0)->(1,1)
        else {
            i1 = 0;
            j1 = 1;
        } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
        // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
        // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
        // c = (3-sqrt(3))/6
        double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        double y1 = y0 - j1 + G2;
        double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
        double y2 = y0 - 1.0 + 2.0 * G2;
        // Work out the hashed gradient indices of the three simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int gi0 = permMod12[ii + perm[jj]];
        int gi1 = permMod12[ii + i1 + perm[jj + j1]];
        int gi2 = permMod12[ii + 1 + perm[jj + 1]];
        // Calculate the contribution from the three corners
        double t0 = 0.5 - x0 * x0 - y0 * y0;
        if (t0 > 0) {
            double t0_2 = t0 * t0;
            double t0_3 = t0_2 * t0;
            double t0_4 = t0_2 * t0_2;
            Grad gr = grad3[gi0];
            double d = dot(gr, x0, y0);
            gradient.x += t0_4 * gr.x - 8 * t0_3 * x0 * d;
            gradient.y += t0_4 * gr.y - 8 * t0_3 * y0 * d;
        }
        double t1 = 0.5 - x1 * x1 - y1 * y1;
        if (t1 > 0) {
            double t1_2 = t1 * t1;
            double t1_3 = t1_2 * t1;
            double t1_4 = t1_2 * t1_2;
            Grad gr = grad3[gi1];
            double d = dot(gr, x1, y1);
            gradient.x += t1_4 * gr.x - 8 * t1_3 * x1 * d;
            gradient.y += t1_4 * gr.y - 8 * t1_3 * y1 * d;
        }
        double t2 = 0.5 - x2 * x2 - y2 * y2;
        if (t2 > 0) {
            double t2_2 = t2 * t2;
            double t2_3 = t2_2 * t2;
            double t2_4 = t2_2 * t2_2;
            Grad gr = grad3[gi2];
            double d = dot(gr, x2, y2);
            gradient.x += t2_4 * gr.x - 8 * t2_3 * x2 * d;
            gradient.y += t2_4 * gr.y - 8 * t2_3 * y2 * d;
        }
        // The result is scaled to return values in the interval [-1,1].
        gradient.scale(70.0);
    }

    /**
     * Calculate the noise value at a point in 3D space.
     */
    public static double noise(double xin, double yin, double zin) {
        double n0, n1, n2, n3; // Noise contributions from the four corners
        // Skew the input space to determine which simplex cell we're in
        double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
        int i = fastfloor(xin + s);
        int j = fastfloor(yin + s);
        int k = fastfloor(zin + s);
        double t = (i + j + k) * G3;
        double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
        double Y0 = j - t;
        double Z0 = k - t;
        double x0 = xin - X0; // The x,y,z distances from the cell origin
        double y0 = yin - Y0;
        double z0 = zin - Z0;
        // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        // Determine which simplex we are in.
        int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
        int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
        if (x0 >= y0) {
            if (y0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // X Y Z order
            else if (x0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // X Z Y order
            else {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // Z X Y order
        } else { // x0<y0
            if (y0 < z0) {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Z Y X order
            else if (x0 < z0) {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Y Z X order
            else {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // Y X Z order
        }
        // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
        // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
        // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
        // c = 1/6.
        double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
        double y1 = y0 - j1 + G3;
        double z1 = z0 - k1 + G3;
        double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
        double y2 = y0 - j2 + 2.0 * G3;
        double z2 = z0 - k2 + 2.0 * G3;
        double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
        double y3 = y0 - 1.0 + 3.0 * G3;
        double z3 = z0 - 1.0 + 3.0 * G3;
        // Work out the hashed gradient indices of the four simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int gi0 = permMod12[ii + perm[jj + perm[kk]]];
        int gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];
        int gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];
        int gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];
        // Calculate the contribution from the four corners
        double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
        if (t0 < 0)
            n0 = 0.0;
        else {
            t0 *= t0;
            n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
        }
        double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
        if (t1 < 0)
            n1 = 0.0;
        else {
            t1 *= t1;
            n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
        }
        double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
        if (t2 < 0)
            n2 = 0.0;
        else {
            t2 *= t2;
            n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
        }
        double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
        if (t3 < 0)
            n3 = 0.0;
        else {
            t3 *= t3;
            n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to stay just inside [-1,1]
        return 32.0 * (n0 + n1 + n2 + n3);
    }

    /**
     * Calculate the gradient of the noise function at a point in 3D space.
     *
     * @param gradient      this is set equal to the gradient of the noise function
     * @param xin           the x coordinate at which to evaluate the function
     * @param yin           the y coordinate at which to evaluate the function
     * @param zin           the z coordinate at which to evaluate the function
     */
    public static void noiseGradient(Vector3d gradient, double xin,
            double yin, double zin) {
        // Skew the input space to determine which simplex cell we're in
        double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
        int i = fastfloor(xin + s);
        int j = fastfloor(yin + s);
        int k = fastfloor(zin + s);
        double t = (i + j + k) * G3;
        double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
        double Y0 = j - t;
        double Z0 = k - t;
        double x0 = xin - X0; // The x,y,z distances from the cell origin
        double y0 = yin - Y0;
        double z0 = zin - Z0;
        // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        // Determine which simplex we are in.
        int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
        int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
        if (x0 >= y0) {
            if (y0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // X Y Z order
            else if (x0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // X Z Y order
            else {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // Z X Y order
        } else { // x0<y0
            if (y0 < z0) {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Z Y X order
            else if (x0 < z0) {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Y Z X order
            else {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // Y X Z order
        }
        // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
        // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
        // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
        // c = 1/6.
        double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
        double y1 = y0 - j1 + G3;
        double z1 = z0 - k1 + G3;
        double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
        double y2 = y0 - j2 + 2.0 * G3;
        double z2 = z0 - k2 + 2.0 * G3;
        double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
        double y3 = y0 - 1.0 + 3.0 * G3;
        double z3 = z0 - 1.0 + 3.0 * G3;
        // Work out the hashed gradient indices of the four simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int gi0 = permMod12[ii + perm[jj + perm[kk]]];
        int gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];
        int gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];
        int gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];
        // Calculate the contribution from the four corners
        gradient.set(0.0, 0.0, 0.0);
        double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
        if (t0 > 0) {
            double t0_2 = t0 * t0;
            double t0_3 = t0_2 * t0;
            double t0_4 = t0_2 * t0_2;
            Grad gr = grad3[gi0];
            double d = dot(gr, x0, y0, z0);
            gradient.x += t0_4 * gr.x - 8 * t0_3 * x0 * d;
            gradient.y += t0_4 * gr.y - 8 * t0_3 * y0 * d;
            gradient.z += t0_4 * gr.z - 8 * t0_3 * z0 * d;
        }
        double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
        if (t1 > 0) {
            double t1_2 = t1 * t1;
            double t1_3 = t1_2 * t1;
            double t1_4 = t1_2 * t1_2;
            Grad gr = grad3[gi1];
            double d = dot(gr, x1, y1, z1);
            gradient.x += t1_4 * gr.x - 8 * t1_3 * x1 * d;
            gradient.y += t1_4 * gr.y - 8 * t1_3 * y1 * d;
            gradient.z += t1_4 * gr.z - 8 * t1_3 * z1 * d;
        }
        double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
        if (t2 > 0) {
            double t2_2 = t2 * t2;
            double t2_3 = t2_2 * t2;
            double t2_4 = t2_2 * t2_2;
            Grad gr = grad3[gi2];
            double d = dot(gr, x2, y2, z2);
            gradient.x += t2_4 * gr.x - 8 * t2_3 * x2 * d;
            gradient.y += t2_4 * gr.y - 8 * t2_3 * y2 * d;
            gradient.z += t2_4 * gr.z - 8 * t2_3 * z2 * d;
        }
        double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
        if (t3 > 0) {
            double t3_2 = t3 * t3;
            double t3_3 = t3_2 * t3;
            double t3_4 = t3_2 * t3_2;
            Grad gr = grad3[gi3];
            double d = dot(gr, x3, y3, z3);
            gradient.x += t3_4 * gr.x - 8 * t3_3 * x3 * d;
            gradient.y += t3_4 * gr.y - 8 * t3_3 * y3 * d;
            gradient.z += t3_4 * gr.z - 8 * t3_3 * z3 * d;
        }
        // The result is scaled to stay just inside [-1,1]
        gradient.scale(32.0);
    }

    /**
     * Calculate a vector valued noise function at a point in 3D space.  This function is
     * closely related to the simplex noise function, but is generally less smooth.  Nonetheless,
     * it is useful in many cases where a random vector is needed at each point in space.
     * The length of the vector is typically on the order of 1.
     *
     * @param v      this is set equal to the value of the noise function
     * @param xin    the x coordinate at which to evaluate the function
     * @param yin    the y coordinate at which to evaluate the function
     * @param zin    the z coordinate at which to evaluate the function
     */
    public static void noiseVector(Vector3d v, double xin, double yin,
            double zin) {
        // Skew the input space to determine which simplex cell we're in
        double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
        int i = fastfloor(xin + s);
        int j = fastfloor(yin + s);
        int k = fastfloor(zin + s);
        double t = (i + j + k) * G3;
        double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
        double Y0 = j - t;
        double Z0 = k - t;
        double x0 = xin - X0; // The x,y,z distances from the cell origin
        double y0 = yin - Y0;
        double z0 = zin - Z0;
        // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        // Determine which simplex we are in.
        int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
        int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
        if (x0 >= y0) {
            if (y0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // X Y Z order
            else if (x0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // X Z Y order
            else {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // Z X Y order
        } else { // x0<y0
            if (y0 < z0) {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Z Y X order
            else if (x0 < z0) {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Y Z X order
            else {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // Y X Z order
        }
        // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
        // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
        // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
        // c = 1/6.
        double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
        double y1 = y0 - j1 + G3;
        double z1 = z0 - k1 + G3;
        double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
        double y2 = y0 - j2 + 2.0 * G3;
        double z2 = z0 - k2 + 2.0 * G3;
        double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
        double y3 = y0 - 1.0 + 3.0 * G3;
        double z3 = z0 - 1.0 + 3.0 * G3;
        // Work out the hashed gradient indices of the four simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int gi0 = permMod12[ii + perm[jj + perm[kk]]];
        int gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];
        int gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];
        int gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];
        // Calculate the contribution from the four corners
        v.set(0.0, 0.0, 0.0);
        double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
        if (t0 > 0) {
            t0 *= t0;
            t0 *= t0;
            Grad gr = grad3[gi0];
            v.x += t0 * gr.x;
            v.y += t0 * gr.y;
            v.z += t0 * gr.z;
        }
        double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
        if (t1 > 0) {
            t1 *= t1;
            t1 *= t1;
            Grad gr = grad3[gi1];
            v.x += t1 * gr.x;
            v.y += t1 * gr.y;
            v.z += t1 * gr.z;
        }
        double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
        if (t2 > 0) {
            t2 *= t2;
            t2 *= t2;
            Grad gr = grad3[gi2];
            v.x += t2 * gr.x;
            v.y += t2 * gr.y;
            v.z += t2 * gr.z;
        }
        double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
        if (t3 > 0) {
            t3 *= t3;
            t3 *= t3;
            Grad gr = grad3[gi3];
            v.x += t3 * gr.x;
            v.y += t3 * gr.y;
            v.z += t3 * gr.z;
        }
        v.scale(6.0);
    }

    /**
     * Calculate the noise value at a point in 4D space.
     */
    public static double noise(double x, double y, double z, double w) {

        double n0, n1, n2, n3, n4; // Noise contributions from the five corners
        // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
        double s = (x + y + z + w) * F4; // Factor for 4D skewing
        int i = fastfloor(x + s);
        int j = fastfloor(y + s);
        int k = fastfloor(z + s);
        int l = fastfloor(w + s);
        double t = (i + j + k + l) * G4; // Factor for 4D unskewing
        double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
        double Y0 = j - t;
        double Z0 = k - t;
        double W0 = l - t;
        double x0 = x - X0; // The x,y,z,w distances from the cell origin
        double y0 = y - Y0;
        double z0 = z - Z0;
        double w0 = w - W0;
        // For the 4D case, the simplex is a 4D shape I won't even try to describe.
        // To find out which of the 24 possible simplices we're in, we need to
        // determine the magnitude ordering of x0, y0, z0 and w0.
        // The method below is a good way of finding the ordering of x,y,z,w and
        // then find the correct traversal order for the simplex we're in.
        // First, six pair-wise comparisons are performed between each possible pair
        // of the four coordinates, and the results are used to add up binary bits
        // for an integer index.
        int c1 = (x0 > y0) ? 32 : 0;
        int c2 = (x0 > z0) ? 16 : 0;
        int c3 = (y0 > z0) ? 8 : 0;
        int c4 = (x0 > w0) ? 4 : 0;
        int c5 = (y0 > w0) ? 2 : 0;
        int c6 = (z0 > w0) ? 1 : 0;
        int c = c1 + c2 + c3 + c4 + c5 + c6;
        int i1, j1, k1, l1; // The integer offsets for the second simplex corner
        int i2, j2, k2, l2; // The integer offsets for the third simplex corner
        int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
        // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
        // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
        // impossible. Only the 24 indices which have non-zero entries make any sense.
        // We use a thresholding to set the coordinates in turn from the largest magnitude.
        // The number 3 in the "simplex" array is at the position of the largest coordinate.
        i1 = simplex[c][0] >= 3 ? 1 : 0;
        j1 = simplex[c][1] >= 3 ? 1 : 0;
        k1 = simplex[c][2] >= 3 ? 1 : 0;
        l1 = simplex[c][3] >= 3 ? 1 : 0;
        // The number 2 in the "simplex" array is at the second largest coordinate.
        i2 = simplex[c][0] >= 2 ? 1 : 0;
        j2 = simplex[c][1] >= 2 ? 1 : 0;
        k2 = simplex[c][2] >= 2 ? 1 : 0;
        l2 = simplex[c][3] >= 2 ? 1 : 0;
        // The number 1 in the "simplex" array is at the second smallest coordinate.
        i3 = simplex[c][0] >= 1 ? 1 : 0;
        j3 = simplex[c][1] >= 1 ? 1 : 0;
        k3 = simplex[c][2] >= 1 ? 1 : 0;
        l3 = simplex[c][3] >= 1 ? 1 : 0;
        // The fifth corner has all coordinate offsets = 1, so no need to look that up.
        double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
        double y1 = y0 - j1 + G4;
        double z1 = z0 - k1 + G4;
        double w1 = w0 - l1 + G4;
        double x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
        double y2 = y0 - j2 + 2.0 * G4;
        double z2 = z0 - k2 + 2.0 * G4;
        double w2 = w0 - l2 + 2.0 * G4;
        double x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
        double y3 = y0 - j3 + 3.0 * G4;
        double z3 = z0 - k3 + 3.0 * G4;
        double w3 = w0 - l3 + 3.0 * G4;
        double x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
        double y4 = y0 - 1.0 + 4.0 * G4;
        double z4 = z0 - 1.0 + 4.0 * G4;
        double w4 = w0 - 1.0 + 4.0 * G4;
        // Work out the hashed gradient indices of the five simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int ll = l & 255;
        int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
        int gi1 = perm[ii + i1
                + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
        int gi2 = perm[ii + i2
                + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
        int gi3 = perm[ii + i3
                + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
        int gi4 = perm[ii + 1
                + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
        // Calculate the contribution from the five corners
        double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
        if (t0 < 0)
            n0 = 0.0;
        else {
            t0 *= t0;
            n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
        }
        double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
        if (t1 < 0)
            n1 = 0.0;
        else {
            t1 *= t1;
            n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
        }
        double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
        if (t2 < 0)
            n2 = 0.0;
        else {
            t2 *= t2;
            n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
        }
        double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
        if (t3 < 0)
            n3 = 0.0;
        else {
            t3 *= t3;
            n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
        }
        double t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
        if (t4 < 0)
            n4 = 0.0;
        else {
            t4 *= t4;
            n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
        }
        // Sum up and scale the result to cover the range [-1,1]
        return 27.0 * (n0 + n1 + n2 + n3 + n4);
    }

    private static class Grad {
        double x, y, z, w;

        Grad(double x, double y, double z) {
            this .x = x;
            this .y = y;
            this .z = z;
        }

        Grad(double x, double y, double z, double w) {
            this.x = x;
            this.y = y;
            this.z = z;
            this.w = w;
        }
    }
    
    
}